Risk and Return

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Chapter 11

• Risk and Return

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Integrated Case Merrill Finch

• Assume that you recently graduated with a major
  in finance and you just landed a job as a
  financial planner with Merrill Finch Inc., a
  large financial services corporation. Your first
  assignment is to invest 100,000 for a client.
  Because the funds are to be invested in a
  business at the end of one year, you have been
  instructed to plan for a one-year holding period.
  Further, your boss has restricted you to the
  following investment alternatives, shown with
  their probabilities and associated outcomes.
  (Disregard for now the items at the bottom of the
  data you will fill in the blanks later.)
•  
• Merrill Finchs economic forecasting staff has
  developed probability estimates for the state of
  the economy, and its security analysts have
  developed a sophisticated computer program which
  was used to estimate the rate of return on each
  alternative under each state of the economy.
  High Tech Inc. is an electronics firm
  Collections Inc. collects past-due debts and
  U.S. Rubber manufactures tires and various other
  rubber and plastics products. Merrill Finch also
  maintains an index fund which owns a
  market-weighted fraction of all publicly traded
  stocks you can invest in that fund, and thus
  obtain average stock market results. Given the
  situation as described, answer the following
  questions.

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• Expected Returns
• Probability Distributions A listing of all
  possible outcomes or events, with each event
  assigned a probability or chance of occurrence.
• Discreet distributions The example above is a
  discreet distribution There are a finite number
  of possible outcomes.
• Why is the T-bills rate of return independent of
  the state of the economy?
• Why are High Techs returns expected to move with
  the economy while Collections are expected to
  move counter to the economy?

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• Expected Rate of Return
•  
• Defn Expected return is the rate of return
  expected from an investment. It is equal to the
  weighted average of all outcomes.
•  
• Formula
•  
• For the examples above
• T-Bills

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• High Tech
• Collections
• Note that expected return does NOT have to be a
  possible outcome.
• Total Return Expected return Unexpected
  return

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Risk

• Exposure to possible loss or injury The chance
  that returns will be lower than expected.
• Stand Alone Risk The risk you face if you owned
  only one asset.
• Variance and Standard Deviation

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• T-Bills

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• High tech
• Collections

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• The Coefficient of Variation (CV) A
  standardized measure of the risk of an investment
  measuring risk per unit of return.
• Example Which would you prefer?

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• For This Case Problem
• T-Bills
• High Tech
• Collections

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Risk Aversion

• An Example
• Which would you prefer
• Salary A has the same expected value as B but
  less risk.

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• Risk Aversion We will assume that investors are
  risk averse.
• Investors when faced with two or more projects
  with the same expected return choose the
  investment with the lower risk.
• When faced with projects of equal risk, choose
  the project with greater expected returns.
• In general investors require higher returns for
  taking on more risk.

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Portfolio Returns and Risk

• Expected Returns
• The expected return of a portfolio of different
  securities is the weighted average return of the
  different securities.

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• Example
• Create a two-stock portfolio by investing 50,000
  in High Tech and 50,000 in collections. What is
  the expected return on this portfolio?

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• Method 1

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• Method 2

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• Cont.
• Risk
• Since we have two stocks with known standard
  deviations why not take the weighted average of
  the standard deviations?

Wrong!!!!
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• Instead view the portfolio like any other stock.
• Note that the risk of the portfolio is
  significantly less than that of either security
  in the portfolio. How can that be?
• High Tech and collections are negatively
  correlated
• By combining securities we actually eliminate
  some risk
• (diversification)

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Capital Asset Pricing Model (CAPM)

• Lets categorize investment risk into two
  categories

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• From an Investors perspective which risk is
  relevant?
• The only risk that is relevant is the risk that
  can not be diversified away.
• Required return risk free rate risk premium
• Market risk can not be diversified away

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Average annualstandard deviation ()
49.2
Diversifiable risk
23.9
19.2
Nondiversifiablerisk
Number of stocksin portfolio
1
10
20
30
40
1000
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• The capital asset pricing model (CAPM)
• Investors are risk averse therefore they expect a
  higher return for higher risk investments.
• The relevant risk is market risk
• Required Rates of Return (CAPM)

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• More on beta
• Beta measure market (systematic) risk
• Beta is measured by examining the sensitivity of
  security returns to market returns.
• ? 1 then a stock has average risk
• The beta of the market portfolio is 1.00
• ? gt 1 then a stock has above average risk
• ? lt 1 then a stock has below average risk
• Examples

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• The risk return relationship for portfolios
• The relationship between risk and rates of return
• E(Ri ) expected rate of return on the ith stock 
• ri Required rate of return on the ith stock.
  For you to purchase a stock this must be less
  than or equal to the expected rate of return. 
• Rf risk-free rate of return. In this context
  RF is usually measured as the return on long-term
  T-bonds or T-bills. 
• ?i a stocks beta or amount of systematic risk
• E(RM) expected rate of return on a market
  portfolio. 
• RPM (RM-RF) risk premium on the market or a
  stock with a ? 1.00.
• RPi (ki-kRF) ? i RPM (? i) risk premium on
  the ith stock.

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• For our example
• High Tech
• Market

1.00
0.00
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• US Rubber
• T-Bills
• Collections

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The Security Market Line (SML)

• Plots the CAPM Plots required returns vs.
  beta.

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SML ri Rf ?i(RM-Rf)
RM15
Rf8
Beta
0
1.0
0.68
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• What about our portfolio?

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• Sifts in the SML
• What happens when inflation increases?

SML ri Rf ?i(RM-Rf)
RM15
Rf8
Beta
1.0
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• What would happen if investors become more risk
  averse?

SML ri Rf ?i(RM-Rf)
RM15
Rf8
Beta
1.0
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• I. Total return - the expected return the
  unexpected return.
• II. Total risk - the variance (or the standard
  deviation) of an assets return.
• III. Systematic and unsystematic risks
• Systematic risks are unanticipated events that
  affect almost all assets to some degree.
• Unsystematic risks are unanticipated events that
  affect single assets or small groups of assets.
• IV. The effect of diversification - the
  elimination of unsystematic risk via the
  combination of assets into a portfolio.
• V. The systematic risk principle and beta - the
  reward for bearing risk depends only on its level
  of systematic risk.
• VI. The capital asset pricing model - E(Ri) Rf
  E(RM) - Rf bi.

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The Efficient Market Hypothesis (EMH)

• Defn Capital markets are informationally
  efficient if
• The stock market is always in equilibrium
• Price value
• If it is impossible to continuously beat the
  market
• What is the implication of this definition?
• Investors on average should earn average returns

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• Forms
• Weak Form Efficiency All information contained
  in past price movements is fully reflected in the
  current stock price.
• Chartists and technical analysts
• Professionals that make investments by examining
  and analyzing trends in stock price data trying
  to identify repeatable trends.
• If the market is weak form efficient what can be
  said about the forecasting ability of chartists?
• Evidence

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• The semi-strong form of the EMH states that
  current prices reflect all publicly available
  information.
• What is public information
• Earnings announcements
• Dividend announcements
• Any info from past WSJ etc.
• Sometimes the value of new information is
  uncertain
• Evidence

Price ()
220 180 140 100
Days relativeto announcement day
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• Strong Form Efficiency The stock price of a
  company already reflects all public information
  and all private information
• What constitutes private information?
• Closed door negotiations
• Undisclosed research findings
• And information internal to management
• Evidence

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• A Diagram of the hypothesis

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So Whats The Point?

• Are markets efficient or have experts figured it
  out?
• Perfect Timing What if at the beginning of the
  year you could predict which investment would
  perform the better An investment in t-bills or
  an investment in the stock market (Small Company
  Stocks)?
• A 1000 investment made 1/1/1926 in 30 day
  t-bills would be worth 12,186 by 12/31/1994.
• A 1000 investment made 1/1/1926 in small company
  stocks would be worth 2,842,773 by 12/31/1994

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• Lets define perfect timing as the ability to tell
  at the beginning of the year whether small
  company stocks or t-bills would perform better
  for the upcoming year.
• At the beginning of the year switch your
  investment to the one with the higher return.
• How much would the same 1000 investment grow too
  if we timed the market perfectly?
• What if we could time the market monthly?

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The End